Pia’s marks in Year 10 assessments are shown - HSC - SSCE Mathematics Standard - Question 5 - 2024 - Paper 1

To find out in which subject Pia performed best compared to the rest of Year 10, we will calculate the Z-scores for her marks in each subject. The formula for the Z-score is given by:

$Z = \frac{(X - \mu)}{\sigma}$

Where:

• $X$ is Pia's mark,
• $\mu$ is the Year 10 mean,
• $\sigma$ is the Year 10 standard deviation.

1. English:
   $Z_{English} = \frac{(78 - 66)}{6} = \frac{12}{6} = 2$

2. Mathematics:
   $Z_{Mathematics} = \frac{(80 - 71)}{10} = \frac{9}{10} = 0.9$

3. Science:
   $Z_{Science} = \frac{(77 - 70)}{15} = \frac{7}{15} \approx 0.47$

4. History:
   $Z_{History} = \frac{(85 - 72)}{9} = \frac{13}{9} \approx 1.44$